A113857 a(n) = binomial(4+2*n, n) * binomial(9+2*n, 4+n).

126, 2772, 48048, 772200, 12033450, 184940756, 2824549728, 43028530272, 655081791000, 9977399586000, 152112583402560, 2322021633001200, 35496198345658050, 543418421128852500, 8331507823355640000, 127919340117331963200, 1966759854303978934200, 30279186980267369086800

Offset: 0

Author

Zerinvary Lajos, Feb 02 2006

Keywords

• easy
• nonn
• changed

Comments

If one uses the "table" view of array A062190, the sequence appears as the fourth column right from the middle in the "formatted as a triangular array" subpanel.

Examples

			a(0) = C(4+2*n,n)*C(9+2*n,4+n) = C(4,0)*C(9,4) = 1*126 = 126.
a(7) = C(4+2*7,7)*C(9+2*7,4+7) = C(18,7)*C(23,11) = 31824*1352078 = 43028530272.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A001700, A002694, A062190.

Programs

Mathematica

a[n_] := Binomial[4+2*n, n] * Binomial[9+2*n, 4+n]; Array[a, 20, 0] (* Amiram Eldar, Sep 05 2025 *)

PARI

a(n)={binomial(4+2*n, n) * binomial(9+2*n, 4+n)} \\ Andrew Howroyd, Jan 07 2020

Formula

a(n) = A062190(4+2*n, 4+n).

a(n) = A002694(n+2)*A001700(n+4). - R. J. Mathar, Nov 28 2008

a(n) ~ 2^(4*n+13) / (Pi*n). - Amiram Eldar, Sep 05 2025

Extensions

Definition rephrased by R. J. Mathar, Nov 28 2008

Edited and more terms added by Andrew Howroyd, Jan 07 2020